ECON 101 FALL 2015 EXAM 1 NAME:______________________________ 1. Suppose the price elasticity of demand for cheeseburgers equals 1.37. This means the overall demand for cheeseburgers is: A) price elastic. B) price inelastic. C) price unit-elastic. D) perfectly price inelastic. 2. The price elasticity of demand for skiing lessons in New Hampshire is less than 1.00. This means that the demand is ______ in New Hampshire. A) price elastic B) price inelastic C) price unit-elastic D) perfectly price elastic 3. If the demand for textbooks is price inelastic, which of the following would explain this? A) Many alternative textbooks can be used as substitutes. B) Students have a lot of time to adjust to price changes. C) Textbook purchases consume a large portion of most students’ income. D) The good is a necessity. 4. A major state university in the South recently raised tuition by 12%. An economics professor at this university asked his students, “Due to the increase in tuition, how many of you will transfer to another university?” One student out of about 300 said that he or she would transfer. Based on this information, the price elasticity of demand for education at this university is: (Hint: one out of 300 is how much of a percentage change? Which percentage change is greater – tuition or transfer? Apply the basic formula for elasticity that I put on the board a few times.) A) one. B) highly elastic. C) highly inelastic. D) zero. 5. Suppose the price elasticity of demand for fishing lures equals 1 in South Carolina and 0.63 in Alabama. To increase revenue, fishing lure manufacturers should: (Hint: If the demand for a product is inelastic, the price can go up and you’ll still buy it, since there are no or few substitutes. If the demand for a product is elastic, the price can go up and you’ll probably walk away from it, since substitutes are available. How might this info impact the pricing strategies of firms?) A) lower prices in each state. B) raise prices in each state. C) lower prices in South Carolina and raise prices in Alabama. D) leave prices unchanged in South Carolina and raise prices in Alabama. Read your syllabus and answer questions 6 through 10: 6. T or F: Disruptive classroom behavior includes the following: chatting with fellow students, use of electronic devices such as laptops, tablets, notebooks, and cell phones, reading or studying during class, sleeping, arriving late, departing early, studying for another class, or in any other way disturbing the class. 7. T or F: It’s OK to use my computer in class or play with my phone. There is no penalty attached to these activities and Keiser doesn’t really mind. 8. T or F: It’s OK to show up late for class and disrupt one of Keiser’s swashbuckling lectures. 9. T or F: Attendance is highly optional since it doesn’t impact my final course grade. 10. T or F: I should blow off the career plan/business plan assignment in this course because it’s unimportant to my future and not worth many points. 11. Jacquelyn is a student at a major state university. Which of the following is not an example of an explicit, or direct, cost of her attending college? A) Tuition B) Textbooks C) the salary that she could have earned working full time D) computer lab fees 12. The two principles of tax fairness are: A) the minimize distortions principle and the maximize revenue principle. B) the benefits principle and the ability-to-pay principle. C) the proportional tax principle and the ability-to-pay principle. D) the equity principle and the efficiency principle. 13. The benefits principles says: A) the amount of tax paid depends on the measure of value. B) those who benefit from public spending should bear the burden of the tax that pays for that spending. C) those with greater ability to pay should pay more tax. D) those who benefit from the tax should pay the same percentage of the tax base as those who do not benefit. 14. A tax that rises less than in proportion to income is described as: (Hint: This would have more of a negative impact on lower income earners vs. higher income earners.) A) progressive. B) proportional. C) regressive. D) structural. 15. The U.S. income tax is _______, while the payroll tax is _______. (Hint: Think income tax vs. Social Security tax.) A) progressive; progressive C) regressive; progressive B) progressive; regressive D) regressive; regressive 16. Who is currently leading in the polls to receive the Republican nomination as that party’s presidential candidate? A) Qasem Soleimani B) Abu Bakr al-Baghdadi C) Osama bin Laden D) Donald J. Trump 17. The single most important thing I’ve learned in class this term is: A) stay in frickin’ school B) stay in school and make a plan for life and my career C) the use of cheese for skyscraper construction D) both A and B above 18. Market equilibrium occurs when: A) there is no incentive for prices to change in the market. B) quantity demanded equals quantity supplied. C) the market clears. D) all of the above occur. 19. Excess supply occurs when: (Hint: Draw a supply and demand graph! Think about price ceilings and floors and the graphs of these we discussed in class.) A) the price is above the equilibrium price. B) the quantity demanded exceeds the quantity supplied. C) the price is below the equilibrium price. D) both b and c occur. 20. The single most important thing I’ve learned in class this term is: a. stay in school and look into either a study abroad or internship experience b. stay in school and make a plan for life and my career c. the untimely demise of Cecil the lion in Zimbabwe d. both a. and b. above 21. According to the textbook definition, mainstream microeconomics generally focuses on a. how individual decision-making units, like households and firms, make economic decisions. b. the performance of the national economy and policies to improve this performance. c. the relationship between economic and political institutions. d. the general level of prices in the national economy. 22. Which of the following is the best summary of the three basic economic questions? a. Who? Why? and When? b. What? How? and Who? c. When? Where? and Why? d. What? Where? and Who? 23. Which of the following is not one of the basic economic resources? a. land b. labor c. capital d. cheese e. entrepreneurship 24. The largest country in the Arabian Peninsula and home to the cities of Riyadh, Jeddah, Mecca, and Medina is: a. The Kingdom of Saudi Arabia b. California c. Spain d. Kentucky 25. T or F: The law of demand explains the upward slope of the supply curve. 26. In economics, a “marginal” value refers to: a. the value associated with an important or marginal activity. b. a value entered as an explanatory item in the margin of a balance sheet or other accounts. c. the value associated with one more unit of an activity. d. a value that is most appropriately identified in a footnote. 27. A government mandated price that is below the market equilibrium price is sometimes called. . . (Hint: Draw a graph again and think about what the government is trying to accomplish.) a. a price ceiling. b. a price floor. c. a market clearing price. d. a reservation price. 28. T or F: Entering the US job market without any education or training is crazy and should be avoided. Stay in frickin’ school, baby! 29. The law of demand states that, other things equal: a. as the price increases, the quantity demanded will increase. b. as the price decreases, the demand curve will shift to the right. c. as the price increases, the quantity demanded will decrease. d. none of the above. 30. The law of supply says: a. other things equal, the quantity supplied of a good is inversely related to the price of the good. b. other things equal, the supply of a good creates its own demand. c. other things equal, the quantity supplied of a good is positively related to the price of the good. d. none of the above. 31. A perfectly inelastic demand curve is: a. horizontal. b. downward sloping. c. upward sloping. d. vertical. 32. A trade-off involves weighing costs and benefits. a. true b. false 33. A perfectly elastic demand curve is: a. horizontal. b. downward sloping. c. upward sloping. d. vertical. 34. The second most important thing I’ve learned in class this term is: a. despair is not an option b. Donald J. Trump’s hair is real c. the use of cheese for skyscraper construction d. none of the above 35. T or F: Virtually any news item has important economic dimensions and consequences. 36. T or F: When studying economics, always think in terms of historical context. 37. This popular Asian country is populated by 1.3 billion people, has the world’s second largest economy, and uses a language that’s been in continuous use for nearly 5,000 years: a. Kentucky b. California c. Spain d. China 38. T or F: The top priority in my life right now should be my education and an internship experience. Without these, the job market is going to kick my butt! 39. Which of the following is a key side effect generated by the use of price ceilings? a. black markets b. products with too high of quality c. an excess supply of a good d. too many resources artificially channeled into the production of a good 40. Which of the following is NOT one of the four basic principles for understanding individual choice? a. Resources are scarce. b. The real cost of something is the money that you must pay to get it. c. “How much?” is a decision at the margin. d. People usually take advantage of opportunities to make themselves better off. 41. A hot mixture of pan drippings, flour, and water is commonly known as: a. interest rates and expected future real GDP. b. interest rates and current real GDP. c. inflation and expected future real GDP. d. gravy. 42. The example we used in class when discussing the inefficiency of quantity quotas was: a. Uber b. General Electric c. AT&T d. the KSU marching band 43. The term we learned in class signifying a key method of non-price competition is: a. excess supply chain management b. arbitrage c. swashbuckling d. product differentiation 44. When discussing market failure and the role of regulation in class, which company/product did we use as an example? a. Pabst Blue Ribbon b. JetBlue c. Blue Bell d. Blue Apron 45. Governments may place relatively high sales taxes on goods such as alcohol and tobacco because: a. such taxes are a significant source of revenue b. such goods exhibit inelastic demand c. such taxes may discourage use of these products d. all of the above 46. When discussing the cost of higher education in class, which country did we cite as an example of one that offers free college for qualifying students? a. USSR b. Rhodesia c. Czechoslovakia d. Germany 47. Which of the following is not an example of market failure we discussed in class? a. externalities b. public goods c. fungible goods d. common pool resources e. equity 48. T or F: As we discussed in class, the real reason why the US has lost jobs to China is the “most favored nation” (MFN) trading status granted to China by the US back in the 1980s. 49. The dude we talked about in class who coined the expression “invisible hand” and promoted self-interest and competition in his famous book “The Wealth of Nations” is: a. Abu Bakr al-Baghdadi b. Ali Khamenei c. Donald J. Trump d. Adam Smith 50. When studying for your final exams and attempting to allocate your limited time among several subjects in order to maximize your course grades (recall, we talked about this example during the first week of class), you’re almost unconsciously engaging in a form of: a. fraud b. miscellaneous serendipity b. mitosis d. marginal analysis

One reason that research on Type A Personality was so popular for so long may be because research on it was funded by ________. the government the alcohol industry the pharmaceutical industry the tobacco industry

Which of the following are stored in the lysosomes of the cell? digestive enzymes glycoproteins being prepared for secretion from the cell material to make ribosomes enzymes for detoxifying harmful compounds such as alcohol chlorophyll for photosynthesis

Critical Thinking: How much stress is too much? The level of stress a person can experience before it does harm to the human body remains an important question. In a study of medical students, many working between 70-80 hours per week, nearly half suffered from extremely high levels of stress. In general, the more hours worked, the greater the level of stress experienced by the student. Higher levels of stress often corresponded with unhealthy coping strategies, including drug and alcohol abuse (Kasi et al., 2007) In addition, the study found that the students’ stress level also put their patients at risk. Stressed residents were more likely to make errors and to compromise patient care (Pitt et al., 2004).

Statistical Methods (STAT 4303) Review for Final Comprehensive Exam Measures of Central Tendency, Dispersion Q.1. The data below represents the test scores obtained by students in college algebra class. 10,12,15,20,13,16,14 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) Q.2. The data below represents the test scores obtained by students in English class. 12,15,16,18,13,10,17,20 Calculate (a) Mean (b) Median (c) Mode (d) Variance, s2 (e) Coefficient of variation (CV) (f) Compare the results of Q.1 and Q.2, Which scores College Algebra or English do you think is more precise (less spread)? Q.3 Following data represents the score obtained by students in one of the exams 9, 13, 14, 15, 16, 16, 17, 19, 20, 21, 21, 22, 25, 25, 26 Create a frequency table to calculate the following descriptive statistics (a) mean (b) median (c) mode (d) first and third quartiles (e) Construct Box and Whisker plot. (f) Comment on the shape of the distribution. (g) Find inter quartile range (IQR). (h) Are there any outliers (based on IQR technique)? In the above problem, if the score 26 is replaced by 37 (i) What will happen to the mean? Will it increase, decrease or remains the same? (j) What will be the new median? (k) What can you say about the effect of outliers on mean and median? Q.4 Following data represents the score obtained by students in one of the exams 19, 14, 14, 15, 17, 16, 17, 20, 20, 21, 21, 22, 25, 25, 26, 27, 28 Create a frequency table to calculate the following descriptive statistics a) mean b) median c) mode d) first and third quartiles e) Construct Box and Whisker plot. f) Comment on the shape of the distribution. g) Find inter quartile range (IQR). h) Are there any outliers (based on IQR technique)? In the above problem, if the score 28 is replaced by 48 i) What will happen to the mean? Will it increase, decrease or remains the same? j) What will be the new median? k) What can you say about the effect of outliers on mean and median? Q.5 Consider the following data of height (in inch) and weight(in lbs). Height(x) Frequency 50 2 52 3 55 2 60 4 62 3  Find the mean height.  What is the variance of height? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.6. The following table shows the number of miles run during one week for a sample of 20 runners: Miles Mid-value (x) Frequency (f) 5.5-10.5 1 10.5-15.5 2 15.5-20.5 3 20.5-25.5 5 25.5-30.5 4 (a) Find the average (mean) miles run. (Hint: Find mid-value of mile range first) (b) What is the variance of miles run? Also, find the standard deviation. (c) Find the coefficient of variation (CV). Q.7. (a) If the mean of 20 observations is 20.5, find the sum of all observations? (b) If the mean of 30 observations is 40, find the sum of all observations? Probability Q.8 Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. a) How many students are in both classes? b) What is the probability that a randomly-chosen student from this group is taking only the Chemistry class? Q.9 A drawer contains 4 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and then replaced. Another ball is taken from the drawer. What is the probability that (Draw tree diagram to facilitate your calculation). (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q.10 A drawer contains 3 red balls, 5 green balls, and 5 blue balls. One ball is taken from the drawer and not replaced. Another ball is then taken from the drawer. Draw tree diagram to facilitate your calculation. What is the probability that (a) both balls are red (b) first ball is red (c) both balls are of same colors (d) both balls are of different colors (e) first ball is red and second ball is blue (f) first ball is red or blue Q. 11 Missile A has 45% chance of hitting target. Missile B has 55% chance of hitting a target. What is the probability that (i) both miss the target. (ii) at least one will hit the target. (iii) exactly one will hit the target. Q. 12 A politician from D party speaks truth 65% of times; another politician from rival party speaks truth 75% of times. Both politicians were asked about their personal love affair with their own office secretary, what is the probability that (i) both lie the actual fact . (ii) at least one will speak truth. (iii) exactly one speaks the truth. (iv) both speak the truth. Q.13 The question, “Do you drink alcohol?” was asked to 220 people. Results are shown in the table. . Yes No Total Male 48 82 Female 24 66 Total (a) What is the probability of a randomly selected individual being a male also drinks? (b) What is the probability of a randomly selected individual being a female? (c) What is the probability that a randomly selected individual drinks? (d) A person is selected at random and if the person is female, what is the probability that she drinks? (e) What is the probability that a randomly selected alcoholic person is a male? Q.14 A professor, Dr. Drakula, taught courses that included statements from across the five colleges abbreviated as AH, AS, BA, ED and EN. He taught at Texas A&M University – Kingsville (TAMUK) during the span of five academic years AY09 to AY13. The following table shows the total number of graduates during AY09 to AY13. One day, he was running late to his class. He was so focused on the class that he did not stop for a red light. As soon as he crossed through the intersection, a police officer Asked him to stop. ( a ) It is turned out that the police officer was TAMUK graduate during the past five years. What is the probability that the Police Officer was from ED College? ( b ) What is the probability that the Police Officer graduated in the academic year of 2011? ( c ) If the traffic officer graduated from TAMUK in the academic year of 2011(AY11). What is the conditional probability that he graduated from the ED college? ( d ) Are the events the academic year “AY 11” and the college of Education “ED” independent? Yes or no , why? Discrete Distribution Q.15 Find k and probability for X=2 and X=4. X 1 2 3 4 5 P(X=x) 0.1 3k 0.2 2k 0.2 (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers.What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Q.16 Find k. X 3 4 5 6 7 P(X=x) k 2k 2k k 2k (Hint: First find k, and then plug in) Also, calculate the expected value of X, E(X) and variance V(X). A game plan is derived based on above table, a player wins $5 if he can blindly choose 3 and loses $1 if he chooses other numbers. What is his expected win or loss per game? If he plays this game for 20 times, what is total win or lose? Binomial Distribution: Q.17 (a) Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover? (b) A (blindfolded) marksman finds that on the average he hits the target 4 times out of 5. If he fires 4 shots, what is the probability of (i) more than 2 hits? (ii) at least 3 misses? (c) which of the following are binomial experiments? Explain the reason. i. Telephone surveying a group of 200 people to ask if they voted for George Bush. ii. Counting the average number of dogs seen at a veterinarian’s office daily. iii. You take a survey of 50 traffic lights in a certain city, at 3 p.m., recording whether the light was red, green, or yellow at that time. iv. You are at a fair, playing “pop the balloon” with 6 darts. There are 20 balloons. 10 of the balloons have a ticket inside that say “win,” and 10 have a ticket that says “lose.” Normal Distribution Q.18 Use standard normal distribution table to find the following probabilities: (a) P(Z<2.5) (b) P(Z< -1.3) (c) P(Z>0.12) (d) P(Z> -2.15) (e) P(0.11 ?)=0.87 (d) P(Z> ?)=0.34 Q.20. The length of life of certain type of light bulb is normally distributed with mean=220hrs and standard deviation=20hrs. (a) Define a random variable, X A light bulb is randomly selected, what is the probability that (b) it will last will last more than 207 hrs. ? (c) it will last less than 214 hrs. (d) it will last in between 199 to 207 hrs. Q.21. The length of life of an instrument produced by a machine has a normal distribution with a mean of 22 months and standard deviation of 4 months. Find the probability that an instrument produced by this machine will last (a) less than 10 months. (b) more than 28 months (c) between 10 and 28 months. Distribution of sample mean and Central Limit Theorem (CLT) Q.22 It is assumed that weight of teenage student is normally distributed with mean=140 lbs. and standard deviation =15 lbs. A simple random sample of 40 teenage students is taken and sample mean is calculated. If several such samples of same size are taken (i) what could be the mean of all sample means. (ii) what could be the standard deviation of all sample means. (iii) will the distribution of sample means be normal ? (iv) What is CLT? Write down the distribution of sample mean in the form of ~ ( , ) 2 n X N   . Q.23 The time it takes students in a cooking school to learn to prepare seafood gumbo is a random variable with a normal distribution where the average is 3.2 hours and a standard deviation of 1.8 hours. A sample of 40 students was investigated. What is the distribution of sample mean (express in numbers)? Hypothesis Testing Q.24 The NCHS reported that the mean total cholesterol level in 2002 for all adults was 203 with standard deviation of 37. Total cholesterol levels in participants who attended the seventh examination of the Offspring in the Framingham Heart Study are summarized as follows: n=3,00, =200.3. Is there statistical evidence of a difference in mean cholesterol levels in the Framingham Offspring (means does the result form current examination differs from 2002 report)?? (Follow the steps below to reach the conclusion) (i) Define null and alternate hypothesis (Also write what is  , and x in words at the beginning) (ii) Identify the significance level ,  and check whether it is one sided or two sided test. (iii) Calculate test statistics, Z. (iv) Use standard normal table to find the p-value and state whether you reject or accept (fail to reject) the null hypothesis. (v) what is the critical value, do you reject or accept the H0. (vi) Write down the conclusion based on part (iv). Q.25 A sample of 145 boxes of Kellogg’s Raisin Bran contain in average 1.95 scoops of raisins. It is known from past experiments that the standard deviation for the number of scoops of raisins is 0.25. The manufacturer of Kellogg’s Raisin Bran claimed that in average their product contains more than 2 scoops of raisins, do you reject or accept the manufacturers claim (follow all five steps)? Q.26 It is assumed that the mean systolic blood pressure is μ = 120 mm Hg. In the Honolulu Heart Study, a sample of n = 100 people had an average systolic blood pressure of 130.1 mm Hg. The standard deviation from the population is 21.21 mm Hg. Is the group significantly different (with respect to systolic blood pressure!) from the regular population? Use 10% level of significance. Q.27 A CEO claims that at least 80 percent of the company’s 1,000,000 customers are very satisfied. Again, 100 customers are surveyed using simple random sampling. The result: 73 percent are very satisfied. Based on these results, should we accept or reject the CEO’s hypothesis? Assume a significance level of 0.05. Q.28 True/False questions (These questions are collected from previous HW, review and exam problems, see the previous solutions for answers) (a) Total sum of probability can exceed 1. (b) If you throw a die, getting 2 or any even number are independent events. (c) If you roll a die for 20 times, the probability of getting 5 in 15th roll is 20 15 . (d) A student is taking a 5 question True-False quiz but he has not been doing any work in the course and does not know the material so he randomly guesses at all the answers. Probability that he gets the first question right is 2 1 . (e) Typing in laptop and writing emails using the same laptop are independent events. (f) Normal distribution is right skewed. (g) Mean is more robust to outliers. So mean is used for data with extreme values. (h) It is possible to have no mode in the data. (i) Standard normal variable, Z has some unit. (j) Only two parameters are required to describe the entire normal distribution. (k) Mean of standard normal variable, Z is 1. (l) If p-value of more than level of significance (alpha), we reject the H0. (m) Very small p-value indicates rejection of H0. (n) H0 always contains equality sign. (o) CLT indicates that distribution of sample mean can be anything, not just normal. (p) Sample mean is always equal to population mean. (q) Variance of sample mean is less than population mean. (r) Variance of sample mean does not depend on sample size. (s) Mr. A has cancer but a medical doctor diagnosed him as “no cancer”. It is a type I error. (t) Level of significance is probability of making type II error. (u) Type II error can be controlled. (v) Type I error is more serious than type II error. (w) Type I and Type II errors are based on null hypothesis. Q.29 Type I and Type II Errors : Make statements about Type I (False Positive) and Type II errors (False Negative). (a) The Alpha-Fetoprotein (AFP) Test has both Type I and Type II error possibilities. This test screens the mother’s blood during pregnancy for AFP and determines risk. Abnormally high or low levels may indicate Down syndrome. (Hint: Take actual status as down syndrome or not) Ho: patient is healthy Ha: patient is unhealthy (b) The mechanic inspects the brake pads for the minimum allowable thickness. Ho: Vehicles breaks meet the standard for the minimum allowable thickness. Ha: Vehicles brakes do not meet the standard for the minimum allowable thickness. (c) Celiac disease is one of the diseases which can be misdiagnosed or have less diagnosis. Following table shows the actual celiac patients and their diagnosis status by medical doctors: Actual Status Yes No Diagnosed as celiac Yes 85 5 No 25 105 I. Calculate the probability of making type I and type II error rates. II. Calculate the power of the test. (Power of the test= 1- P(type II error) Answers: USEFUL FORMULAE: Descriptive Statistics Possible Outliers, any value beyond the range of Q 1.5( ) and Q 1.5( ) Range = Maximum value -Minimum value 100 where 1 ( ) (Preferred) 1 and , n fx x For data with repeats, 1 ( ) (Preferred ) OR 1 and n x x For data without repeats, 1 3 1 3 3 1 2 2 2 2 2 2 2 2 2 2 Q Q Q Q x s CV n f n f x x OR s n fx nx s n x x s n x nx s                             Discrete Distribution         ( ) ( ) ( ) ( ) { ( )} ( ) ( ) 2 2 2 2 E X x P X x V X E X E X E X xP X x Binomial Distribution Probability mass function, P(X=x)= x n x n x C p q  for x=0,1,2,…,n. E(X)=np, Var(X)=npq Hypothesis Testing based on Normal Distribution      X std X mean Z Standard Normal Variable, Probability Bayes Rule, ( ) ( and ) ( ) ( ) ( | ) P B P A B P B P A B P A B    Central Limit Theorem For large n (n>30), ~ ( , ) 2 n X N   and ˆ ~ ( , ) n pq p N p For hypothesis testing of μ, σ known           n x Z   For hypothesis testing of p n pq p p Z   ˆ ANSWERS: Q.1 (a) 14.286 (b) 14 (c) none (d) 10.24 (e) 22.40 Q.2 (a) 15.125 (b) 15.5 (c) No (d) 10.98 (e) 21.9 (f) English Q.3 (a) 18.6 (b)19 (c) 16, 21, and 25 (d) 15, 22 (f) slightly left (g) 7 (h) no outliers (i) increase (j) same Q.4 (a) 0.41 (b) 20 (c)14, 17, 20, 21,25 (d) 16.5, 25 (f) slightly right (g) 8.5 (h) no (i) increase (j) same Q.5 (a)56.57 (b) 22.26 (c) 8.34 Q.6 (a) 21 (b) 38.57 (c) 29.57 Q.7 (a) 410 (b) 1200 Q.8 (a)3 (b) 0.65 Q.9 (a) 0.082 (b) 0.29 (c)0.34 (d) 0.66 (e)0.10 (f) 0.64 Q.10 (a) 0.038 (b)0.23 (c) 0.71 (d) 0.29 (e)0.096 (f) 0.62 Q.11 (i)0.248 (ii)0.752 (iii)0.505 Q.12 (i)0.0875 (ii)0.913 (iii)0.425 (iii)0.488 Q.13 (a)0.22 (b)0.41 (c)0.33 (d)0.27 (e) 0.67 Q.14 (a) 0.13 (b) 0.18 (c)0.12 Q.15 E(X)=3.1 , V(X)=1.69, $0.2 per game, $ 4 win. Q.16 E(X)=5.125, V(X)=1.86, $0.25 loss per game, $5 loss. Q.17 (a)0.201 (b) 0.819, 0.027 Q.18 (a)0.9938 (b)0.0968 (c)0.452 (d)0.984 (e) 0.0433 (f)0.2353 Q.19 (a) -0.25 (b)0.71 (c) -1.13 (d)0.41 Q.20 (b) 0.7422 (c) 0.3821 (d) 0.1109 Q.21 (a)0.0014 (b) 0.0668 (c) 0.9318 Q.22 (a) 140 (b)2.37 Q.24 Z=-1.26, Accept null. Q.25 Z=-2.41, accept null Q.26 Z=4.76, reject H0 Q.27 Z=-1.75, reject H0 Q.28 F, F, F, T , F, F, F, T, F, T, F, F, T, T, F, F, T, F, T, F, F, T, T Q.29 (c)0.113 , 0.022 , 0.977 (or 98%)

One reason that research on Type A Personality was so popular for so long may be because research on it was funded by ________. the government the alcohol industry the pharmaceutical industry the tobacco industry

Physics 2010 Sid Rudolph Fall 2009 MIDTERM 4 REVIEW Problems marked with an asterisk (*) are for the final. Solutions are on the course web page. 1. A. The drawing to the right shows glass tubing, a rubber bulb and two bottles. Is the situation you see possible? If so, carefully describe what has taken place in order to produce the situation depicted. B. The picture depicts three glass vessels, each filled with a liquid. The liquids each have different densities, and DA > DB > DC. In vessel B sits an unknown block halfway to the bottom and completely submerged. 1. _______ In which vessel would the block sit on the bottom? 2. _______ In which vessel would the block float on the top? 3. _______ In which vessel would the block feel the smallest buoyant force? 4. _______ In which vessels are buoyant forces on the block are the same? 5. _______ Assume the coefficient of volume expansion for the liquid in B and the block are $B > $block. If the temperature of vessel B with the block is raised, would block B rise to the surface, sink to the bottom, or remain where it is? 2. A circular tank with a 1.50 m radius is filled with two fluids, a 4.00 m layer of water and a 3.00 m layer of oil. Use Doil = 8.24 × 10 kg/m and Dwater = 1.00 × 10 kg/m , and Datm = 1.01 × 10 N/m . 2 3 3 3 5 2 A. What are the gauge and absolute pressures 1.00 m above the bottom of the tank? B. A block of material in the shape of a cube (m = 100 kg and side length = 42.0 cm) is released at the top of the oil layer. Where does the block come to rest? Justify your answer. If it comes to rest between two layers, specify which layers and what portion of the block sits in each layer. [Note: Vcube = a ]3 C. A small 1.00 cm radius opening is made in the side of the tank 0.500 m up from its base (block was removed). What volume of water drains from the tank in 10.0 s? (b) (a) 3. A tube is inserted into a vein in the wrist of a patient in a reclined position on a hospital bed. The heart is vertically 25.0 cm above the position of the wrist where the tube is inserted. Take DBLOOD = 1.06 × 103 kg/m3. The gauge venous blood pressure at the level of the heart is 6.16 × 103 N/m2. Assume blood behaves as an ideal nonviscous fluid. A. What is the gauge venous blood pressure at the position of the wrist? B. The tube coming from the wrist is connected to a bottle of whole blood the patient needs in a transfusion. See above figure (b). What is the minimum height above the level of the heart at which the bottle must be held to deliver the blood to the patient? C. Suppose the bottle of blood is held 1.00 m above the level of the heart. Assume the tube inserted in the wrist has a diameter of 2.80 mm. What is the velocity, v, and flow rate of blood as it enters the wrist. You may also assume the rate at which the blood level in the bottle drops is very small. The answer you get here is a substantial overstatement. Blood is not really a non-viscous fluid. 4. A 0.500 kg block is attached to a horizontal spring and oscillates back and forth on a frictionless surface with a frequency of f = 3.00 hz. The amplitude of this motion is 6.00 × 10 m. Assume to = 0 and is the instant the block is -2 at the equilibrium position moving to the left. A. Write expressions x(t) = !A sin (Tt) and v(t) = !AT cos (Tt) filling in the values of A and T. B. What is the total mechanical energy (METOT) of the block-spring system? C. Suppose the block, at the moment it reaches its maximum velocity to the left splits in half with only one of the halves remaining attached to the spring. What are the amplitude and frequency of the resulting oscillations? D. Suppose, instead of splitting at the position of maximum velocity to the left, the block now splits when it is at the extreme position in the left. What are the amplitude and frequency of the resulting motion? E. Describe in words what would happen to the period of oscillation if a second block identical to the first block were dropped on the first block at either of its extreme positions. 5. A. A spring has one end attached to a wall and the other end attached to two identical masses, mA and mB. The system is set into oscillation on a frictionless surface with amplitude A. See figure. When the system is momentarily at rest at x = -A whatever it is that holds mA to mB fails; and later in the motion mB moves away from mA to the right. 1. Location where the acceleration of mA is maximum and negative. 2. Location where the KE of mA is maximum. The next few questions ask you to compare the behavior of the mass-spring system after and before mB detached. Energy considerations are most useful here. 3. The amplitude of the mass-spring oscillation has (increased, decreased, not changed) after mB detaches. 4. The frequency of the mass-spring oscillation has (increased, decreased, stayed the same) after mB detaches. 5. The maximum speed of mA has (increased, decreased, stayed the same) after mB detaches. 6. The period of oscillation of the mass-spring system has (increased, decreased, stayed the same) after mB detaches. 7. The fraction of the total mechanical energy of the entire spring-2 mass system carried away with mB after mB detaches is B. A spherical object is completely immersed in a liquid and is neutrally buoyant some distance above the bottom of the vessel. See figure. The upper surface of the liquid is open to the earth’s atmosphere. 1. How is the density of the fluid related to the density of the spherical object? 2. Assume the fluid and object are incompressible. In addition, the $sphere (coefficient of volume expansion) > $liquid. For the following items below, indicate whether the object sinks to the bottom, rises to the surface, or does nothing based on the changes described. a. Atmospheric pressure drops by 20%. b. Salt is dissolved in the liquid in the same way fresh water is turned into salt water. c. The entire apparatus is warmed 10oC (liquid and object are both warmed). d. The entire apparatus is transported to the surface of the moon. (gmoon = 1.6 m/s , PATM = 0 on moon) 2 e. 100 cm3 of the liquid is removed from the top. The object is still initially submerged. 6. A. A mass m is attached to a spring and oscillating on a frictionless, horizontal surface. See figure. At the instant the mass passes the equilibrium position moving to the right, half the mass detaches from the other half. The oscillating system is now the spring and half the original mass with the detached mass moving off to the right with constant velocity. Relative to the original spring-mass system, the new spring-mass system with half the mass oscillates with … In the spaces provided below, enter the words larger, smaller or the same that best completes the above sentence.. 1. amplitude 2. period 3. frequency 4. maximum velocity 5. mechanical energy B. A solid cylinder is floating at the interface between water and oil with 3/4 of the cylinder in the water region and 1/4 of the cylinder in the oil region. See figure. Select the item in the parenthesis that best fits the statement. 1. The item (oil, water, and/or cylinder) with the largest density. 2. The item (oil, water, and/or cylinder) with the smallest density. 3. The weight of the cylinder (is equal to, greater than or less than) the total buoyant force it feels. 4. The density of the cylinder (is equal to, less than, or greater than) the density of water. rC. Three thermometers in different settings record temperatures T1 = 1000°F, T2 = 1000°C, and T3 = 1000 K. In the space below select T1, T2 or T3, that best fits the statement. 1. The thermometer in the hottest environment. 2. The thermometer in the coolest environment. 3. The thermometer reading a temperature 900° above the boiling point of water. 7. An oil tanker in the shape of a rectangular solid is filled with oil (Doil = 880 kg/m ). The flat bottom of the 3 hull is 48.0 m wide and sits 26.0 m below the surface of the surrounding water. Inside the hull the oil is stored to a depth of 24.0 m. The length of the tanker, assumed filled with oil along the entire length, is 280 m. View from Rear View from Side Note: Dsalt water = 1.015 × 10 kg/m ; Vrectangular solid = length × width × height. 3 3 A. At the bottom of the hull, what is the water pressure on the outside and the oil pressure on the inside of the horizontal bottom part of the hull? Assume the Po above the oil is the same as the Po above the water and its value is Po = 1.01 × 10 N/m . 5 2 B. If you did part A correctly you determined that the water pressure on the horizontal bottom part of the hull is larger than the oil pressure there. Explain why this MUST be the case. C. What buoyant force does the tanker feel? D. What is the weight of the tanker, excluding the weight of the oil in the hull? 8. A. Water is poured into a tall glass cylinder until it reaches a height of 24.0 cm above the bottom of the cylinder. Next, olive oil (Doil = 920 kg/m ) is very carefully added until the total amount of 3 fluid reaches 48.0 cm above the bottom of the cylinder. Olive oil and water do not mix. See figure. Take Dwater = 1.00 × 10 kg/m and Patm = 1.01 × 10 N/m . 3 3 5 2 1. Indicate on the drawing which layer is water and which is olive oil. 2. What is the gauge pressure 10.0 cm below the top of the upper fluid layer in the cylinder. 3. What is the gauge pressure on the bottom of the cylinder? 4. If the cylinder is in the shape of a right circular cylinder with radius of 3.60 cm, what force is exerted on the bottom of the cylinder? B. A 0.200 kg mass is hung from a massless spring. At equilibrium, the spring stretched 28.0 cm below its unstretched length. This mass is now replaced with a 0.500 kg mass. The 0.500 kg mass is lowered to the original equilibrium position of the 0.200 kg mass and suddenly released producing vertical SHM. 1. What is the spring constant for this spring? 2. What is the period of oscillation for the 0.500 kg/spring system? 3. What is the amplitude of this oscillation? r9. The drawing shows a possible design for a thermostat. It consists of an aluminum rod whose length is 5.00 cm at 20.0°C. The thermostat switches an air conditioner when the end of the rod just touches the contact. The position of the contact can be changed with an adjustment screw. What is the size of the spacing such that the air conditioner turns on at 27.0°C. This is not a very practical device. Take “al = 2.3 × 10 /°C. -5 r10. The following is an effective technique for determining the temperature TF inside a furnace. Inside the furnace is 100 gm of molten (i.e., in a liquid state) lead (Pb). The lead is dropped into an aluminum calorimeter containing 200 gm water both at an initial temperature of 10.0°C. After equilibrium is reached, the temperature reads 21.8°C. Assumptions: (1) No water is vaporized; (2) no heat is lost to or gained from the environment; and (3) the specific heat for the lead is the same whether the lead is a solid or a liquid. DATA TABLE LEAD CALORIMETER WATER mPb = 100 gm mAl = 150 gm mW = 200 gm CPb = 0.0305 cal/gm°C CAl = 0.215 cal/gm°C CW = 1.0 cal/gm°C LF = 6.0 ca./gm (heat of fusion) Tinit = 10.0°C Tinit = 10.0°C MPPb = 327°C (melting point) TF = unknown Tequilibrium = 21.8°C A. In words, describe the distinct steps in the cooling of lead. B. How many calories of heat are absorbed by the calorimeter and the water it contains to reach 21.8°C? C. How many calories are lost by the lead in cooling from TF to the final equilibrium temperature of 21.8°C? D. What was the original furnace temperature? E. If the same amount of aluminum (CAl = 0.215 cal/gm°C and LM = 21.5 cal/gm) were used in the same furnace instead of lead, would the final equilibrium temperature be higher, less or the same as in the lead case? No calculation is needed to answer this. Please explain. r11. The length of aluminum cable between consecutive support towers carrying electricity to a large metropolitan area is 180.00 m on a hot August day when the temperature is 38°C. Use “(Al) = 24 × 10-6/°C. A. What is the length of the same section of aluminum cable on a very cold winter day when T = -24°C? B. If the same length of copper (” = 17 × 10-6/°C) cable (i.e., 180.00 m on the same hot August day) were used instead of aluminum, would the length of the copper cable be shorter, longer or the same as that of the aluminum on the same winter day as in (A)? Please explain your conclusion You do not have to do any calculations here. r12. You wish to make a cup of coffee with cream in a 0.250 kg mug (cmug = 900 J/kg°C) with 0.325 kg coffee (ccoffee = 4.18 × 10 J/kg°C) starting at 25.0°C and 0.010 kg cream (ccream = 3.80 × 10 J/kg°C) at 10.0°C. 3 3 You use a 50.0 W electric heater to bring the coffee, cream and mug to a final temperature of 90.0°C. How long must the coffee system be heated? Indicate clearly the assumptions you need to make. r13. A 75.0 kg patient is running a fever of 106°F and is given an alcohol rubdown to lower his body temperature. Take the specific heat of the human body to be Cbody = 3.48 × 10 J/kg°C, the heat of 3 evaporation of the rubbing alcohol to be Lv(alcohol) = 8.51 × 10 J/kg, and the density of the rubbing 5 alcohol to be 793 kg/m3. You may assume that all the heat removed from the fevered body goes into evaporating the alcohol, and that while the patient’s body is cooling, his metabolism adds no measurable heat. A. What quantity of heat must be removed from the body to lower its temperature to 99.0°F? B. What volume of rubbing alcohol is required? C. This is a qualitative question. Give an answer and explanation. Suppose you were told that the alcohol applied started at room temperature (. 70°F) and were given the specific heat for the alcohol. Thus, you now expect some of the body heat warming the alcohol to the temperature of the fever before evaporation occurs. How would this effect the result of the calculation in part (B)? r14. A 56.0 kg hypothermia victim is running a body temperature of 91.0°F. The victim is far away from any immediate medical treatment. Her friends decide to treat the hypothermia victim by placing the victim in a sleeping bag with one of her friends and use the heat from the friend to raise the victim’s body temperature. Take the specific heat of the human body to be Cbody = 3.48 × 10 J/kg°C. Assume that the sleeping bag acts 3 like a perfect calorimeter and also assume no heat is lost to or obtained from the sleeping bag. Finally, assume all the heat that warms the hypothermia victim comes from the basic metabolic heat produced by the body of the victim’s friend in the sleeping bag with her and that metabolism is rated at 2.00 × 106 cal/day, and that the victim’s metabolism is negligible. A. How much heat must be added to the victim’s body to get her temperature up to 98.0°F? B. How long must the victim remain in the sleeping bag with her friend to achieve this temperature change? C. This is a qualitative question. If the thermal characteristics of the sleeping bag are now taken into account, but still assuming no heat leaves or enters the sleeping bag, how will the answer to question (b) above be different? r15. A few years back a lawsuit was filed by a woman against McDonald’s because she scalded herself with a Styrofoam cup filled with coffee which she spilled on herself while driving. This question was spawned by that incredible legal action and represents a possible action taken by McDonald’s to insure cooler coffee. Suppose a typical cup of coffee sold by McDonald’s is basically 400 ml of hot water and when poured into the Styrofoam cup its temperature is 96.0°C. Take 1.00 ml to have a mass of 1.00 gm and = 4.19 kJ/kg°C. Neglect any heat lost to the cup and assume no heat is lost by the coffee to the environment. A. How much heat in joules must the coffee lose to bring its temperature to a drinkable 68.0°C? B. McDonald’s possible approach to lowering the temperature of the 96.0°C coffee to 68.0°C is to add a cube of ice initially at 0.0°C. (Take Lf = 334 kJ/kg.) What mass of ice has to be added to the coffee to reduce its initial temperature to the desired 68.0°C? r16. During this past Thanksgiving your instructor overdid it and consumed 3000 Cal of food and dessert. Remember 1.0 Cal = 4.19 x 10 J. For the questions below, as 3 sume no heat is lost to the environment. [Note: = 33.5 x 105 J/kg; = 4.19 x 103 J/kgoC] A. If all of this energy went into heating 65.0 kg water starting at 37.0oC (a mass approximately that of your instructor), what would be the final temperature of this water? B. Assume your instructor removes these overeating calories by running 10 kilometer races [note: 1.61 km = 1.00 mile]. Using the rule of thumb that 1 mile of jogging will require 100 Cal, what is the minimum number of races your instructor must run to consume the 3000 Cal in part A as exercise? C. The year before, your instructor was particularly gluttonous and consumed 5000 Cal. Assuming the same conditions of water mass (65.0 kg) and starting temperature (37.0oC) as in A, what is the final temperature of the water system, and if any water vaporizes to steam, how much? [Note: BP(H2O) = 100 C] o 17. Below is the position vs. time graph for the simple harmonic of a spring oscillation on a frictionless horizontal surface. Motion to the right is positive. 1. The earliest instant of time, including t0 = 0 at which the PEelastic is maximum. 2. The earliest instant of time at which the KE of the mass is a maximum and the mass is moving to the right. 3. The earliest instant of time at which the acceleration of the mass is maximum and positive. 4. The earliest instant of time at which the speed of the mass is zero. 18. A. A spring is attached to a post at the top of a 15.0° frictionless ramp. A 2.00 kg mass is attached to the spring and the mass is slowly allowed to stretch the spring to the equilibrium position of the mass-spring system, the spring stretches by 0.400 m See figure. The mass is now pulled an additional 10.0 cm and released. The mass-spring system executes simple harmonic motion. 1. What is the spring constant, k, of the spring. 2. What are the amplitude and period of oscillation of the mass-spring system? B. A solid, uniform cylinder is floating at the interface between water (Dwater = 1.00 × 103 kg/m ) and oil (Doil = 8.24 × 10 kg/m ) with 3/4 of the cylinder in the water region and 3 3 3 1/4 of the cylinder in the oil region. Assume the axis of the cylinder is perfectly vertical. See figure. 1. What is the density of the material out of which the cylinder is made? 2. Assume the upper surface of the oil region si open to the atmosphere (Datm = 1.01 × 10 N/m ) and the oil-water interface is 0.500 m below the 5 2 upper surface of the oil. Also assume the height of the cylinder is 10.0 cm. What is the gauge pressure on the bottom surface of the cylinder? Recall: Pgauge = P – PATM. 19. A. A mass m is attached to a spring and is oscillating on a frictionless horizontal surface (see figure). At the instant the mass is at an amplitude position a second identical mass is carefully placed on top of the original mass. The oscillating system is now the spring and the two identical masses. Relative to the original spring-single mass system, the new spring-2-mass system oscillates with a … In the spaces provided below, enter (I) for increased, (D) for decreased, or (R) remains unchanged, that best completes the above last sentence. 1. amplitude. 2. period. 3. frequency. 4. spring constant. 5. maximum speed. 6. mechanical energy. 7. maximum acceleration. B. Suppose you are asked about the absolute pressure at some depth h below the surface of a liquid. The top surface is exposed to the atmosphere on a sunny day in Salt Lake City. For each statement below in the spaces provided, enter I for increase, D for decrease, or R for remains the same, when accounting for what happens to the absolute pressure at the point you are observing. 1. More liquid is added so now the observation point is farther below the surface. 2. The fluid is now exchanged for a less dense fluid. The observation point is at same h. 3. The experiment is moved to New York City, which is at sea level, on a sunny day. 4. The fluid is now seen to be moving with some speed v past the observation point. 5. The observation point is moved closer to the surface of the liquid. 6. The air above the fluid is removed by a vacuum system. 7. The apparatus is moved to a laboratory on the surface of the moon. 20. A 3.00 kg mass is attached to a spring (k = 52.0 N/m) that is hanging vertically from a fixed support. The mass is moved to a position 0.800 m lower than the unstretched position of the end of the spring. The spring is then released and the mass-spring system executes SHM. Take the 0.800 m of the mass as the reference location for its gravitational PE. A. What is the equilibrium position of the mass-spring system? B. What is the amplitude of the SHM the mass-spring system executes? C. What is the period of the oscillation of this system? D. What is the total mechanical energy of the mass-spring system at the moment the mass is released? E. What are (i) the KE of the mass and (ii) the speed of the mass when the spring is at its equilibrium position? 21. A 38.0 kg block is moving back and forth on a frictionless horizontal surface between two springs. The spring on the right has a force constant kR = 2.50 × 10 N/m. When the block is between the two 3 springs its speed (v) is 1.82 m/s. See figure. A. If the block compresses the left spring to 5.62 cm beyond its uncompressed length, determine the value of kL. B. What is the maximum compression of the right spring when the mass interacts with it? C. What is the total time the spring on the right is compressed during a single event? 22. Two identical containers are connected at the bottom via a tube of negligible volume and a valve which is closed. Both containers are filled initially to the same height of 1.00 m, one with chloroform (DC = 1530 kg/m ) in the left chamber and the other 3 with mercury in the right chamber (DHg = 1.36 × 10 kg/m ). 4 3 Sitting on top of each identical circular container is a massless plate that can slide up or down without friction and without allowing any fluid to leak past. The radius of the circular plate is 12.0 cm. The valve is now opened. A. What volume of mercury drains into the chloroform container? (Note: Vcyl = Br h) 2 B. What mass must be placed on the plate on the chloroform side to force all the mercury, but none of the chloroform, back to the mercury chamber? 23. A 12.0 kg mass M is attached to a cord that is wrapped around a wheel in the shape of a uniform disk of radius r = 12.0 cm and mass m = 10.0 kg. The block starts from rest and accelerates down the frictionless incline with constant acceleration. Assume the disk axle is frictionless. Note: Idisk = 1/2 mr . 2 A. Use energy methods to find the velocity of the block after it has moved 2.00 m down the incline. B. What is the constant acceleration of the block and the angular acceleration of the wheel? C. How many revolutions does the wheel turn for the distance the block travels in (A)? D. If the uniform disk were replaced by a uniform sphere with the same r and m of the disk, would the acceleration of the block attached to the sphere be larger, smaller, or the same as that for the block attached to the disk? Note: Isphere = 2/5 mr . 2 24. A pulley is in the shape of a uniform disk of mass m = 5.00 kg and radius r = 6.40 cm. The pulley can rotate without friction about an axis through the center of mass. A massless cord is wrapped around the pulley and connected to a 1.80 kg mass. The 1.80 kg mass is released from rest and falls 1.50 m. See figure. Note: Idisk = 1/2 mr . 2 A. Use energy methods to determine the speed of the block after falling 1.50 m. B. What is the constant acceleration of the block and the angular acceleration of the wheel? C. How many revolutions does the pulley disk turn for the distance the block travels in (A)? D Suppose the disk were replaced by a uniform sphere with the same r and m of the disk. Would the acceleration of the block attached to the sphere be larger, smaller, or the same as that for the block attached to the the disk? Note: Isphere 2/5 mr . 2 26. A 700.0 N fisherman is walking toward the edge of a 200 N plank as shown. He has placed a can of worms weighing 75.0 N on the left side of the plank as indicated in the drawing. The plank is the horizontal section in the drawing. A. Identify all the forces the plank feels before it begins to tip. Draw a free body diagram. B. As the fisherman nears the point on the plank where it begins to tip, how do the upward forces the supports exert on the plank change. C. How far a distance, as measured from the center of the right support, can he walk before the plank begins to tip? 26. A 75.0 kg sign hangs from a 4.80 m uniform horizontal rod whose mass is 120 kg. The rod is supported by a cable that makes an angle of 53° with the rod. he sign hangs 3.60 m out along the rod. A. What is the tension in the cable? B. What are the forces PPv and PPH exerted by the wall on the left end of the rod? 27. A 1.00 × 104 N great white shark is hanging by a cable attached to a 4.00 m massless rod that can pivot at its base. See figure. A. Determine the tension in the cable supporting the upper end of the rod. See figure. B. Determine the force (a vector quantity) exerted on the base of the rod. Suggestion: Find this force by first evaluating the separate components of the force. See figure. 28. A 6.00 m uniform beam extends horizontally from a hinge fixed on a wall on the left. A cable is attached to the right end of the beam. The cable makes an angle of 30.0° with respect to the horizontal and the right end of the cable is fixed to a wall on the right. At the right end of the cable hangs a 140.0 kg mass. The mass of the beam is 240.0 kg. See figure. A. Find the tension in the cable. B. Find the vertical and horizontal forces the hinge exerts on the left end of the beam. 29 A. The blades of a “Cuisinart” blender when run at the “mix” level, start from rest and reach 2.00 × 103 rpm (revolutions per minute) in 1.60 s. The edges of the blades are 3.10 cm from the center of the circle about which they rotate. 1. What is the angular acceleration of the blades in rad/s2 while they are accelerating? 2. Through how many rotations did the blades travel in that 1.60 s? 3. If the blades have a moment of inertia of 5.00 × 10-5 kg m2, what net torque did the blades feel while accelerating? B. A 7.50 × 10 N 4 shipping crate is hanging by a cable attached to a uniform 1.20 × 104 N steel beam that can pivot at its base. A second cable supports the beam and is attached to a wall. See figure. 1. Determine the tension T in the upper cable. 2. Determine the magnitude of the force exerted on the beam at its base. See drawing. 30. The drawing shows a uniform ladder of length L and weight 220 N. The ladder is sitting at an angle of 30° above the horizontal resting on the corner of a concrete wall at a point that is one-fourth of the way from the end of the ladder. A 640 N construction worker is standing on the ladder one-third of the way up from the end of the ladder which is resting on the ground. Assume the corner of the wall on which the ladder rests exerts only a normal force on the ladder at the point where there is contact. A. What is the magnitude of the normal force the wall exerts on the ladder? B. Find the magnitude of both the normal force the ground exerts on the left end of the ladder and the static frictional force the ground exerts on the left end of the ladder. 31. A. A solid, right circular cylinder (radius = 0.150 m, height = 0.120 m) has a mass m. The cylinder is floating in a tank in the interface between two liquids that do not mix: water on the bottom and oil above. One-third of the cylinder is in the oil layer (Doil = 725 kg/m ) 3 and two-thirds in the water layer (Dwater = 1.00 × 10 kg/m ). See 3 3 drawing. Note: V(circular cylinder) = B r2 h. 1. Find the mass of the cylinder. 2. With the cylinder present, take the thickness of the oil layer to be 0.200 m and the thickness of the water layer to be 0.300 m. What is the gauge pressure at the bottom of the tank? Assume the top of the oil layer is exposed to the atmosphere. B. A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of T = 7.52 rad/s. The drawing indicates the position of the block when the spring is unstretched. That position is labeled “x = 0 m” in the drawing. The drawing also shows a small bottle whose left edge is located at Xb = 0.0900 m. The block is now pulled to the right, stretching the spring by Xs = 0.0343 m, and is then thrown to the left, i.e., given an initial push to the left. In order for the block to knock over the bottle when it is moving to the right, it must be “thrown” with an initial speed to the left v0. Ignoring the width of the block, what is the minimum value of v0? 32. B. Three objects, a disk (ICM = ½ MR ), a hoop (ICM = MR ), and a hollow ball (ICM = b MR ) all have 2 2 2 the same mass and radius. Each is subject to the same uniform tangential force that causes the object, starting from rest, to rotate with increasing angular speed about an axis through the center of mass for each object. In the case of the hollow ball the tangential force has a moment arm equal to the radius of the ball. In the space below, enter D for disk, H for hoop, and/or B for hollow ball, or same to best answer the question. 1. The object with the largest moment of inertia about the axis through the CM. 2. The object experiencing the greatest net torque. 3. The object with the greatest angular acceleration during the period the force is acting. 4. The object rotating with the smallest angular speed assuming the force has been acting for the same length of time on each object. 33. A. A uniform disk (D), hoop (H), and sphere (S), all with the same mass and radius, can freely rotate about an axis through the center of mass (CM) of each. A massless string is wrapped around each item. The string is used to apply a constant and equal tangential force to each object. See figure. For the statements below, enter D, H, S, none or the same. Assume all objects start from rest at the same instant. 1. The one with the smallest moment of inertia about the shown axis. 2. The object experiencing the largest net torque. 3. The object undergoing the smallest angular acceleration. 4. The object with the largest angular speed after an elapsed time of 5.0 s. 5. The object for which the largest amount of string has unraveled in 5.0 s. 6. The object with the smallest KErot after 5.0 s. 7. The object that undergoes the most rotations in 5.0 s. B. A spherical object is completely immersed in a liquid of density Dliq some distance above the bottom of the vessel. See figure. The upper surface is initially open to the earth’s atmosphere at sea level. Assume the liquid and object are both incompressible. For the items below, indicate whether the object sinks to the bottom (B), rises to the surface (T), or does nothing (N). 1. The vessel is brought to Salt Lake City. 2. Salt is dissolved in the liquid in the same way fresh water is turned into salt water. 3. The top 50 cm3 of the liquid is removed from the vessel. 4. The entire apparatus is transported to the surface of the moon. 5. The volume of the spherical object is increased by heating it without heating the liquid. 6. The spherical object is moved 10 cm farther down in the vessel and released. 7. A mass is placed on the top surface of the liquid in the vessel increasing the pressure at the surface. No fluid leaks. 34. A 2.20 × 103 N uniform beam is attached to an overhead beam as shown in the drawing. A 3.60 × 103 N trunk hangs from an attachment to the beam two-thirds of the way down from the upper connection of the beam to the overhead support. A cable is tied to the lower end of the beam and is also attached to the wall on the right. A. What is the tension in the cable connecting the lower end of the beam to the wall? B. What are magnitude of the vertical and horizontal components of the force the overhead beam exerts on the upper end of the beam at P? 35. A. A 12.0 kg block moves back and forth on a frictionless horizontal surface between two springs. The spring on the right has a force constant k = 825 N/m. When the block arrives at the spring on the right, it compresses that spring 0.180 m from its unstretched position. 1. What is the total mechanical energy of the block and two spring system? 2. With what speed does the block travel between the two springs while not in contact with either spring? 3. Suppose the block, after arriving at the left spring, remains in contact with that spring for a total time of 0.650 s, before separating on its way to the right spring? Using the connection between this 0.650 s and the period of oscillation between the block and the left spring, determine the spring constant of the left spring. B. A turkey baster (see figure) consists of a squeeze bulb attached to a plastic tube. When the bulb is squeezed and released, with the open end of the tube under the surface of the turkey gravy, the gravy rises in the tube to a distance h, as shown in the drawing. It can then be squirted over the turkey. Using Patm = 1.013 × 105 N/m2 for atmospheric pressure and 1.10 × 103 kg/m3 for the density of the gravy, determine the absolute pressure of the air in the bulb with the distance h = 0.160 m. Give answer to three significant digits. 36. A. The pictures below depict three glass vessels, each filled with a liquid. The liquids each have different densities, and DA > DB > DC. In vessel C an unknown block is neutrally buoyant halfway to the bottom and completely submerged. A, B, and/or C, or none are all possible answers. 1. _______ In which vessel(s) would the block sink all the way to the bottom? 2. _______ In which vessel(s) would the largest volume of the block be exposed above the surface of the liquid? 3. _______ In which vessel(s) would the buoyant forces on the block be the same? B. A swinging pendulum (A) and a mass-spring system (B) are built to have identical periods. For the statements below enter either A, B, U (unchanged) to best fit which oscillating system would have the larger period as a result of the change. 1. _______ The mass of the mass-spring system is increased. 2. _______ The mass of the swinging pendulum is increased without altering the location of its center of mass. 3. _______ The spring constant of the mass-spring system is increased. 4. _______ The length of the swinging pendulum system is increased. 5. _______ Both systems are taken to the moon and set oscillating. C. A block of mass m moves back and forth on a frictionless surface between two springs. See drawing. Assume kL > kR. For the statements below enter L for the left spring, R for the right spring, or same as the case may be. 1. _______ The spring that has the maximum compression when m is momentarily at rest. 2. _______ The spring that stores the larger elastic potential energy when maximally compressed. 3. _______ The spring that momentarily stops the block in the least time once the block arrives at the spring. 37. A uniform beam extending at right angles from a wall is used to display an advertising sign for an eatery. The beam is 2.50 m long an weighs 80.0 N. The sign, whose dimensions are 1.00 m by 0.800 m, is uniform, and weighs 200. N, hangs from the beam as shown in the drawing. A cable, attached to the wall of the eatery at a point on the beam where the inside end of the sign is attached to the beam and making an angle of 60.0° with the beam, supports this advertising structure. A. What is the magnitude of the tension in the cable supporting the beam? B. What are the magnitudes of the horizontal and vertical forces the wall exerts on the left end of the beam? 38. A. Examine the picture shown to the right. Initially, before the pump is turned on, the two masses (m1 = 1.00 kg, m2 = 2.75 kg) are held in place. the pressures above and below m1 are Patm = 1.01 × 10 N/m and 5 2 the spring is in its unstretched position. The pump is turned on and the masses are allowed to move. The mass m1 moves without friction inside a cylindrical piston of radius r = 3.85 cm. Once equilibrium is established, by what distance has the spring stretched? Take k = 2.00 × 103 N/m for the spring constant. B. A solid cylinder (radius 0.125 m and height 0.150 m) has a mass of 6.50 kg. The cylinder is floating in water. Oil (Doil = 725 kg/m ) is poured on top of the water until 3 the situation shown in the drawing results. How much of the height (in meters) of the cylinder remains in the water layer?